Energy and Mv^2/2

my confusion is:when a rod fixed about one end with a frictionless hinge rotates through an angle theta height (h) , we use energy conservation methods to find it's velocity (linear or angular)for eg: mgh= 1/2 I ω^2 but never something like mgh=1/2 m v^2 I have used both eqns and both give different valeus of velocity. the ones which match the answers given at the end of the textbooks correspond to the first equation my ques is why can't we use the second eqn??
- bobby (age 17)
scotland

For each little part of mass m, you can use mv^2/2 for its kinetic energy. The problem with trying to use that for the whole rotating object of mass M is that the different parts have different v's. The average of v² over the object is thus bigger than the square of the average v. The rotational version already takes the range of v's into account.

Mike W.

(published on 12/30/2015)